Week 5: Developing mathematics pedagogies that integrate embodied, multisensory, outdoors, and arts-based modalities

“Swish” (The Activity)

It was just last week, when my math department head was excited to share the card game “Swish”.  She explained the basic rules and made me sample a round with her.  Because I was so busy last week, I wasn’t in the mindset to learn, and found it difficult to understand and follow.  But this week, after watching the Ali and Colin’s video on representing binary numbers as concentric circles with coloring, the light switched in my mind, and the motivation to learn the game “Swish” was ignited.  Although my choice in this week's activity is not working with binaries, the colored circles are still there, and the activity embodied the math through playing a game and working their minds.  So, I took my time to read the instructions, watch the YouTube tutorial on “Swish” (https://www.youtube.com/watch?v=Hzi28pbeWWw) and had a couple of my students play the game with me. 

              The card game “Swish” includes 60 transparent swish cards.  We lay out 16 cards, in a hunt to find swishes. A swish is made when a colored circle ball is embedded in the same-colored hoop. Players must only use their minds to mentally rotate, flip and stack the cards to imagine the colored balls in the correct corresponding-colored hoops. When a player finds a match, the participant will say "Swish" and prove the match through the action of rotating, flipping or stacking the cards. Example shown in the picture below.

            My first “Swish” game was with a designated student, whom the EA from day one informed me immediately that the student was "designated", who struggled and had failed Science in semester 1.  To my surprise, the student was quick with his mental capabilities to rotate, flip and stack the cards, leading him victory. He shared his story, how back home in Vietnam, he didn’t have devices to play with, and because of that, he was able to develop his good memory from real live activities and games.

In the second round of Swish, we introduced the game to 3 other players, to see how the experience of the game changes with more players. With more players, it felt more competitive and our bodies hovered over the game cards engaged to think fast.  In a group setting, although my designated student, wasn’t as quick to make the swishes, he had fun socializing and being able to participate in a math game with his peers. This experience shed light on the importance on how extra time and different settings for some students, would reduce anxiety for formative and summative assessments or tasks, and enable equal opportunity of success, for students to showcase their learning.

              An extension of this game could be used in a Pre-Calculus 12 course.  Students tend to have difficulties imagining the transformations of basic trigonometric functions. The Swish game and Vi Hart Music and Braiding videos showed me how transparencies with images and color, are great math visuals for students. I know that powerful computer-generated software like Desmos (https://www.desmos.com/calculator) can transform trig functions in seconds, but I want to see the students embody the learning.  So if students were given a couple of transparencies, they may graph the grid on one transparency, then draw a basic trig function (ex. y = sinX) on a second transparency, and see how the points within the sinX graph changes with movements of translations left/right, flips across x or y axis or any from of compressions or expansions.  Students can explore visually and see how the variables a, h and q, affects the function y = sinX in the function  y = a sin (X - h) + q. While my students explore I can walk around and see what is happening and correct any misconceptions made. Who knew transparencies (what I used in the early 2000's to teach), could make a comeback and be a good resource for students to embody the math. 

Watch my YouTube video for the visual of my extension activity inspired by this week's activity. https://youtu.be/vDa9c0siyb4

What Math Education Can Learn from Art: The Assumptions, Values and Vision of Mathematics Education (Leslie Dietiker)

              In the article What Math Education Can Learn from Art, Dietiker suggests teachers to “perceive mathematics as a form of art”, using the form of storytelling and narratives, giving the typically taught mathematical algorithms and concepts life, to draw students in, placing the focus on “exploration rather than discovery” creating an element of “surprise” rather than “control” (Eisner, 2002).  

The element of “exploration” for my math students to find their “surprise” in math is something I am working on. Because I do like a sense of control and order, I do teach math how I see it, using the story I see in my head, which make sense to me. Recently, I have been working on asking the students to reflect on what they see or understand, sharing their stories with the math taught.  This is something that I am currently working on and exploring with my students for my final project so it results and findings will come by end of this course. 

              I was not surprised to read that between 1995 to 2005, teaching mathematics in the U.S. was dominated by content driven outcomes, losing the freedom to play and create inspirational math experiences with the curriculum. Dietiker noted the influences that the National Council of Teachers in Mathematics (NCTM) 2000 standards resulted in math teachers resorting to teaching mathematics from the textbooks without questioning its order, content, nor structure. From my range of experiences at multiple secondary schools, I have had experience where I am instructed to follow an order because the school had math midterms and finals which students must write. It is within those parameters and working environment, I do feel I am trapped with teaching from the text to cover the content within a certain time frame.  I do notice that when I am teaching a course that has no math textbook, I break from traditional teaching and am able to explore other means to convey the math curriculum. What was funny was that 6 years ago, when I didn’t have a math textbook to teach workplace Math 12, I blended the math with science because of my science background. But now, six years later, gaining student insight from teaching Career Life Courses and now professionally developing with the UBC MAED Master’s program, I am slowly expanding my ideas being learning to blend other disciplines and life experiences in math course to make it more engaging for the students.